Before you can arrive at a bias setting for any given tape, you first need a repeatably measurable parameter. Otherwise even if you arrive at a setting which you consider optimum you'd never be able to repeat it.
The usual measurable parameter used is overbias drop-off at 10kHz. That is, the bias is adjusted for maximum output at 10kHz, and then increased, causing a drop in the output level. How much the output level drops in dB is the amount of overbias drop-off.
In the old days this used to have to be done at a recording level below 0dB VU even at 15ips because of tape saturation at 10kHz, but nowadays with, say, SM468 tape, I have found I can set the 10kHz overbias on my Revox B77 at either 7 1/2 or 15ips at 0dB VU without encountering saturation. I even use a "hot" setting for 0dB VU, corresponding to a fluxivity of 355nW/m on the tape. There's a lot of headroom that can be got from modern tapes. For what it's worth, I use 4dB overbias drop-off at 10kHz with SM468 at 1ips on the Revox B77.
However, please note that you can't transfer an overbias setting from one type of recorder to another unless they use the same recording head (or at the very least, their recording heads have the same gap length). On the Nagra IV-S I use a 10kHz overbias of just 1dB for the same tape at the same speed to achieve what I think is just about the same level of bias on the tape.
Having defined how to quantify the setting and how to achieve it repeatedly and consistently you can then set about finding what you consider to be an optimum setting.
Unfortunately this is not as straightforward, as just about every performance parameter is affected by the bias setting. Briefly:
- Distortion. As bias is varied, there is a value for which minimum distortion is achieved. Unfortunately this varies with frequency. Minimum distortion for a 1kHz signal needs rather higher bias than minimum distortion for a 10kHz signal. So the setting is, unfortunately, a compromise. Tape distortion for low frequency signals is usually quoted as 3rd harmonic distortion (tape overloads symmetrically, a bit like a push-pull amplifier, so any 2nd harmonic in the output is usually caused by single-ended record electronics rather than the tape). Tape distortion for high frequency signals is quoted as intermodulation (IM) distortion, because the third harmonic of 10kHz is inaudible to humans at 30kHz, but, for example, the 1kHz intermodulation difference tone between 10kHz and 11kHz, and the various sums at 8, 9, 12, 13 kHz and so on are definitely audible.
- Saturation. As bias is increased, there is a value for which the level at which the tape saturates (there is no further increase in output level for any increase in input level) reaches a maximum. However, again, this varies with frequency; the saturation maximum is reached with a lower level of bias for high frequencies than for low frequencies.
- Sensitivity and frequency response. As bias is increased, there is once again a maximum in sensitivity which, once again, varies with frequency. In effect, variation of bias affects both recording level and frequency response. The frequency response is corrected by adjusting the record equalisation after adjusting the bias.
So, in practice, and by my experience (there's probably a million ways to do this), you will choose a certain amount of overbias at 10kHz for your chosen type of tape on your machine, adjust the bias, record eq and record level and make some recordings. Start with the machine manufacturer's recommended setting for that tape, or for a similar type of tape from another tape manufacturer. If you find the sound is dynamic, especially in the highs, but seems to be a bit harsh, you probably need more bias. If you find the sound seems smooth, but a bit lacking in dynamics and headroom, especially in the highs, you probably need less bias. Make a measured change in the 10kHz overbias, re-set the eq and level and try again.
Whatever you do, don't try to arrive at a setting by varying bias only, because the change in frequency response and level will mislead you. You must make a complete realignment of the record section of the machine to your chosen new bias level before making a comparison.
Have in mind that the setting you arrive at will also depend on what type of music you record. My recordings of chamber music do not have the same frequency content as somebody else's recordings of highly percussive jazz, for example, or yet someone else's on-location film sound on a Nagra, complete with breaking glass, slamming doors, gunshots or whatever. So it's likely that these different recordings will need different settings of bias and reference level.
An extreme example of this is
Bay Area Studio Engineering's method for biasing a track on a multitrack machine speciallly for kick drum, by having the percussionist play only the kick drum, and listening off tape for minimum distortion. Minimum distortion for the kick drum will probably require significantly more bias than usual, since the kick drum doesn't put out much high frequency content. But other bias settings offering better high frequency headroom or less distortion at high frequencies are of academic interest only for a track with just a kick drum on it.
For further reading, you could do a lot worse than peruse
RMGI's technical data for studio tapes. These show clearly the variation in various performance parameters with bias level and usefully define these parameters.
You could also read
Jay Mc Knight's technical paper on biasing.
I know this is a lot of information to absorb but the rewards are there to be had for putting in the effort. Analogue open reel tape, having been the leading professional medium for half a century, has a long tradition of excellence behind it, backed by real know-how from people who put decades of research and practice into it. We can only be grateful to them for so generously sharing their knowledge and experience.